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421 lines
13 KiB
C++
421 lines
13 KiB
C++
#ifndef CRYPTOPP_INTEGER_H
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#define CRYPTOPP_INTEGER_H
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/** \file */
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#include "cryptlib.h"
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#include "secblock.h"
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#include <iosfwd>
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#include <algorithm>
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NAMESPACE_BEGIN(CryptoPP)
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struct InitializeInteger // used to initialize static variables
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{
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InitializeInteger();
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};
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typedef SecBlock<word, AllocatorWithCleanup<word, CRYPTOPP_BOOL_X86> > IntegerSecBlock;
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//! multiple precision integer and basic arithmetics
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/*! This class can represent positive and negative integers
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with absolute value less than (256**sizeof(word)) ** (256**sizeof(int)).
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\nosubgrouping
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*/
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class CRYPTOPP_DLL Integer : private InitializeInteger, public ASN1Object
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{
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public:
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//! \name ENUMS, EXCEPTIONS, and TYPEDEFS
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//@{
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//! division by zero exception
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class DivideByZero : public Exception
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{
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public:
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DivideByZero() : Exception(OTHER_ERROR, "Integer: division by zero") {}
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};
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//!
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class RandomNumberNotFound : public Exception
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{
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public:
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RandomNumberNotFound() : Exception(OTHER_ERROR, "Integer: no integer satisfies the given parameters") {}
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};
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//!
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enum Sign {POSITIVE=0, NEGATIVE=1};
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//!
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enum Signedness {
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//!
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UNSIGNED,
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//!
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SIGNED};
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//!
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enum RandomNumberType {
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//!
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ANY,
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//!
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PRIME};
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//@}
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//! \name CREATORS
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//@{
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//! creates the zero integer
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Integer();
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//! copy constructor
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Integer(const Integer& t);
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//! convert from signed long
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Integer(signed long value);
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//! convert from lword
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Integer(Sign s, lword value);
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//! convert from two words
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Integer(Sign s, word highWord, word lowWord);
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//! convert from string
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/*! str can be in base 2, 8, 10, or 16. Base is determined by a
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case insensitive suffix of 'h', 'o', or 'b'. No suffix means base 10.
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*/
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explicit Integer(const char *str);
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explicit Integer(const wchar_t *str);
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//! convert from big-endian byte array
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Integer(const byte *encodedInteger, size_t byteCount, Signedness s=UNSIGNED);
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//! convert from big-endian form stored in a BufferedTransformation
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Integer(BufferedTransformation &bt, size_t byteCount, Signedness s=UNSIGNED);
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//! convert from BER encoded byte array stored in a BufferedTransformation object
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explicit Integer(BufferedTransformation &bt);
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//! create a random integer
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/*! The random integer created is uniformly distributed over [0, 2**bitcount). */
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Integer(RandomNumberGenerator &rng, size_t bitcount);
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//! avoid calling constructors for these frequently used integers
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static const Integer & CRYPTOPP_API Zero();
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//! avoid calling constructors for these frequently used integers
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static const Integer & CRYPTOPP_API One();
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//! avoid calling constructors for these frequently used integers
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static const Integer & CRYPTOPP_API Two();
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//! create a random integer of special type
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/*! Ideally, the random integer created should be uniformly distributed
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over {x | min <= x <= max and x is of rnType and x % mod == equiv}.
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However the actual distribution may not be uniform because sequential
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search is used to find an appropriate number from a random starting
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point.
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May return (with very small probability) a pseudoprime when a prime
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is requested and max > lastSmallPrime*lastSmallPrime (lastSmallPrime
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is declared in nbtheory.h).
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\throw RandomNumberNotFound if the set is empty.
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*/
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Integer(RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType=ANY, const Integer &equiv=Zero(), const Integer &mod=One());
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//! return the integer 2**e
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static Integer CRYPTOPP_API Power2(size_t e);
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//@}
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//! \name ENCODE/DECODE
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//@{
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//! minimum number of bytes to encode this integer
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/*! MinEncodedSize of 0 is 1 */
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size_t MinEncodedSize(Signedness=UNSIGNED) const;
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//! encode in big-endian format
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/*! unsigned means encode absolute value, signed means encode two's complement if negative.
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if outputLen < MinEncodedSize, the most significant bytes will be dropped
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if outputLen > MinEncodedSize, the most significant bytes will be padded
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*/
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void Encode(byte *output, size_t outputLen, Signedness=UNSIGNED) const;
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//!
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void Encode(BufferedTransformation &bt, size_t outputLen, Signedness=UNSIGNED) const;
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//! encode using Distinguished Encoding Rules, put result into a BufferedTransformation object
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void DEREncode(BufferedTransformation &bt) const;
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//! encode absolute value as big-endian octet string
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void DEREncodeAsOctetString(BufferedTransformation &bt, size_t length) const;
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//! encode absolute value in OpenPGP format, return length of output
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size_t OpenPGPEncode(byte *output, size_t bufferSize) const;
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//! encode absolute value in OpenPGP format, put result into a BufferedTransformation object
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size_t OpenPGPEncode(BufferedTransformation &bt) const;
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//!
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void Decode(const byte *input, size_t inputLen, Signedness=UNSIGNED);
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//!
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//* Precondition: bt.MaxRetrievable() >= inputLen
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void Decode(BufferedTransformation &bt, size_t inputLen, Signedness=UNSIGNED);
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//!
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void BERDecode(const byte *input, size_t inputLen);
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//!
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void BERDecode(BufferedTransformation &bt);
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//! decode nonnegative value as big-endian octet string
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void BERDecodeAsOctetString(BufferedTransformation &bt, size_t length);
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class OpenPGPDecodeErr : public Exception
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{
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public:
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OpenPGPDecodeErr() : Exception(INVALID_DATA_FORMAT, "OpenPGP decode error") {}
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};
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//!
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void OpenPGPDecode(const byte *input, size_t inputLen);
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//!
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void OpenPGPDecode(BufferedTransformation &bt);
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//@}
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//! \name ACCESSORS
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//@{
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//! return true if *this can be represented as a signed long
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bool IsConvertableToLong() const;
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//! return equivalent signed long if possible, otherwise undefined
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signed long ConvertToLong() const;
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//! number of significant bits = floor(log2(abs(*this))) + 1
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unsigned int BitCount() const;
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//! number of significant bytes = ceiling(BitCount()/8)
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unsigned int ByteCount() const;
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//! number of significant words = ceiling(ByteCount()/sizeof(word))
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unsigned int WordCount() const;
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//! return the i-th bit, i=0 being the least significant bit
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bool GetBit(size_t i) const;
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//! return the i-th byte
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byte GetByte(size_t i) const;
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//! return n lowest bits of *this >> i
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lword GetBits(size_t i, size_t n) const;
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//!
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bool IsZero() const {return !*this;}
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//!
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bool NotZero() const {return !IsZero();}
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//!
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bool IsNegative() const {return sign == NEGATIVE;}
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//!
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bool NotNegative() const {return !IsNegative();}
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//!
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bool IsPositive() const {return NotNegative() && NotZero();}
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//!
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bool NotPositive() const {return !IsPositive();}
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//!
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bool IsEven() const {return GetBit(0) == 0;}
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//!
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bool IsOdd() const {return GetBit(0) == 1;}
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//@}
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//! \name MANIPULATORS
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//@{
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//!
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Integer& operator=(const Integer& t);
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//!
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Integer& operator+=(const Integer& t);
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//!
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Integer& operator-=(const Integer& t);
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//!
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Integer& operator*=(const Integer& t) {return *this = Times(t);}
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//!
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Integer& operator/=(const Integer& t) {return *this = DividedBy(t);}
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//!
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Integer& operator%=(const Integer& t) {return *this = Modulo(t);}
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//!
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Integer& operator/=(word t) {return *this = DividedBy(t);}
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//!
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Integer& operator%=(word t) {return *this = Integer(POSITIVE, 0, Modulo(t));}
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//!
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Integer& operator<<=(size_t);
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//!
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Integer& operator>>=(size_t);
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//!
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void Randomize(RandomNumberGenerator &rng, size_t bitcount);
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//!
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void Randomize(RandomNumberGenerator &rng, const Integer &min, const Integer &max);
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//! set this Integer to a random element of {x | min <= x <= max and x is of rnType and x % mod == equiv}
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/*! returns false if the set is empty */
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bool Randomize(RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType, const Integer &equiv=Zero(), const Integer &mod=One());
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bool GenerateRandomNoThrow(RandomNumberGenerator &rng, const NameValuePairs ¶ms = g_nullNameValuePairs);
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void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs ¶ms = g_nullNameValuePairs)
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{
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if (!GenerateRandomNoThrow(rng, params))
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throw RandomNumberNotFound();
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}
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//! set the n-th bit to value
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void SetBit(size_t n, bool value=1);
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//! set the n-th byte to value
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void SetByte(size_t n, byte value);
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//!
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void Negate();
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//!
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void SetPositive() {sign = POSITIVE;}
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//!
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void SetNegative() {if (!!(*this)) sign = NEGATIVE;}
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//!
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void swap(Integer &a);
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//@}
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//! \name UNARY OPERATORS
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//@{
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//!
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bool operator!() const;
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//!
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Integer operator+() const {return *this;}
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//!
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Integer operator-() const;
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//!
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Integer& operator++();
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//!
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Integer& operator--();
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//!
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Integer operator++(int) {Integer temp = *this; ++*this; return temp;}
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//!
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Integer operator--(int) {Integer temp = *this; --*this; return temp;}
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//@}
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//! \name BINARY OPERATORS
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//@{
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//! signed comparison
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/*! \retval -1 if *this < a
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\retval 0 if *this = a
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\retval 1 if *this > a
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*/
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int Compare(const Integer& a) const;
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//!
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Integer Plus(const Integer &b) const;
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//!
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Integer Minus(const Integer &b) const;
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//!
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Integer Times(const Integer &b) const;
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//!
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Integer DividedBy(const Integer &b) const;
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//!
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Integer Modulo(const Integer &b) const;
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//!
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Integer DividedBy(word b) const;
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//!
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word Modulo(word b) const;
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//!
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Integer operator>>(size_t n) const {return Integer(*this)>>=n;}
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//!
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Integer operator<<(size_t n) const {return Integer(*this)<<=n;}
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//@}
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//! \name OTHER ARITHMETIC FUNCTIONS
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//@{
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//!
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Integer AbsoluteValue() const;
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//!
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Integer Doubled() const {return Plus(*this);}
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//!
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Integer Squared() const {return Times(*this);}
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//! extract square root, if negative return 0, else return floor of square root
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Integer SquareRoot() const;
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//! return whether this integer is a perfect square
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bool IsSquare() const;
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//! is 1 or -1
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bool IsUnit() const;
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//! return inverse if 1 or -1, otherwise return 0
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Integer MultiplicativeInverse() const;
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//! modular multiplication
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CRYPTOPP_DLL friend Integer CRYPTOPP_API a_times_b_mod_c(const Integer &x, const Integer& y, const Integer& m);
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//! modular exponentiation
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CRYPTOPP_DLL friend Integer CRYPTOPP_API a_exp_b_mod_c(const Integer &x, const Integer& e, const Integer& m);
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//! calculate r and q such that (a == d*q + r) && (0 <= r < abs(d))
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static void CRYPTOPP_API Divide(Integer &r, Integer &q, const Integer &a, const Integer &d);
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//! use a faster division algorithm when divisor is short
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static void CRYPTOPP_API Divide(word &r, Integer &q, const Integer &a, word d);
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//! returns same result as Divide(r, q, a, Power2(n)), but faster
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static void CRYPTOPP_API DivideByPowerOf2(Integer &r, Integer &q, const Integer &a, unsigned int n);
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//! greatest common divisor
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static Integer CRYPTOPP_API Gcd(const Integer &a, const Integer &n);
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//! calculate multiplicative inverse of *this mod n
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Integer InverseMod(const Integer &n) const;
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//!
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word InverseMod(word n) const;
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//@}
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//! \name INPUT/OUTPUT
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//@{
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//!
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friend CRYPTOPP_DLL std::istream& CRYPTOPP_API operator>>(std::istream& in, Integer &a);
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//!
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friend CRYPTOPP_DLL std::ostream& CRYPTOPP_API operator<<(std::ostream& out, const Integer &a);
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//@}
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private:
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friend class ModularArithmetic;
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friend class MontgomeryRepresentation;
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friend class HalfMontgomeryRepresentation;
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Integer(word value, size_t length);
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int PositiveCompare(const Integer &t) const;
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friend void PositiveAdd(Integer &sum, const Integer &a, const Integer &b);
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friend void PositiveSubtract(Integer &diff, const Integer &a, const Integer &b);
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friend void PositiveMultiply(Integer &product, const Integer &a, const Integer &b);
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friend void PositiveDivide(Integer &remainder, Integer "ient, const Integer ÷nd, const Integer &divisor);
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IntegerSecBlock reg;
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Sign sign;
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};
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//!
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inline bool operator==(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)==0;}
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//!
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inline bool operator!=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)!=0;}
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//!
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inline bool operator> (const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)> 0;}
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//!
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inline bool operator>=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)>=0;}
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//!
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inline bool operator< (const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)< 0;}
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//!
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inline bool operator<=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)<=0;}
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//!
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inline CryptoPP::Integer operator+(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Plus(b);}
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//!
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inline CryptoPP::Integer operator-(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Minus(b);}
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//!
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inline CryptoPP::Integer operator*(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Times(b);}
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//!
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inline CryptoPP::Integer operator/(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.DividedBy(b);}
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//!
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inline CryptoPP::Integer operator%(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Modulo(b);}
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//!
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inline CryptoPP::Integer operator/(const CryptoPP::Integer &a, CryptoPP::word b) {return a.DividedBy(b);}
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//!
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inline CryptoPP::word operator%(const CryptoPP::Integer &a, CryptoPP::word b) {return a.Modulo(b);}
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NAMESPACE_END
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#ifndef __BORLANDC__
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NAMESPACE_BEGIN(std)
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inline void swap(CryptoPP::Integer &a, CryptoPP::Integer &b)
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{
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a.swap(b);
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}
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NAMESPACE_END
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#endif
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#endif
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